Abilities are made complex for a reason...
Champions are thematic creatures, their abilities need to represent who they are as an identity and what role they place. Take Braum for instance; his leap gives resists so you can jump in an save your teammate, not just for blind complexity. His shield gives movement speed so you can position yourself correctly whilst it's up, not just for blind complexity.
Champions need to have a specific role they fit so that they can be good and bad picks for a team. If Kha'Zix's passive didn't have a slow his jungling wouldn't a be good pick-off assassin. If Thresh's hook didn't have a passive damage component, why wouldn't you pick Blitzcrank all the time?
Finally, champions need counterplay. If douchebag just has s hispells like single target 100% scaling punch there wouldn't provide much counterplay. Abilities have %health damage so you don't max them early but they allow better late game scaling instead of just being OP in lane. Think Rengar before his ult had an indicator; you had no way of knowing he was about to jump on you and 100-0 you real quick unless you had prior vision of him. But now you have the indicator when he is stealthed near you, so you can pop shields, flash, heal, get closer to teammates, time a stun etc.
Simplicity doesn't necessarily make the game balanced/easier/fair.